Affine transformations and bi-anisotropic media in differential-form approach

A class of bi-anisotropic electromagnetic media, form invariant in all spatial affine transformations, is defined using differential-form formalism and called the class of AB media. The four-dimensional medium dyadic defines an eigenvalue problem with two eigenvalues which define two eigenfields. It is shown that any electromagnetic two-form field can be expressed as a sum of eigenfields which appear uncoupled in a homogeneous AB medium. For each of the eigenfields the original bi-anisotropic AB medium can be replaced by a simpler anisotropic effective medium.